Warm Up Use scalar multiplication to evaluate the following:

Section 4.2: Matrix Multiplication

**Multiply rows times columns. **You can only multiply if the number of columns in the 1st matrix is equal to the number of rows in the 2nd matrix. They must match. Dimensions: 3 x 2 2 x 3 The dimensions of your answer.

Examples: 2(3) + -1(5) 2(-9) + -1(7) 2(2) + -1(-6) 3(3) + 4(5) 3(-9) + 4(7) 3(2) + 4(-6)

2 x 2 2 x 2 0(4) + (-1)(-2) 0(-3) + (-1)(5) 1(4) + 0(-2) 1(-3) +0(5) *Answer should be a 2 x 2 2 x 2 2 x 2 0(4) + (-1)(-2) 0(-3) + (-1)(5) 1(4) + 0(-2) 1(-3) +0(5)

*They don’t match so can’t be multiplied together.* Dimensions: 2 x 3 2 x 2 *They don’t match so can’t be multiplied together.*

Systems in Matrix Multiplication Form We can write the following system of equations in Matrix Multiplication Form: Take the coefficients of each of the variables and put them in one matrix The variables go in a second matrix An equal sign separates the product of the previous matrices and the matrix of the solutions

Just to make sure it works…

More Practice Multiply the following matrices: Can you multiply them? Check the dimensions: What should the new dimensions be? Set up the multiplication matrix. R1, C1 = R2, C1

Even More Practice Multiply the following matrices: Can you multiply them? Check the dimensions: What should the new dimensions be? Set up the multiplication matrix. R1, C1 R1, C2 = R2, C1 R2, C2 R3, C1 R2, C2